How does economic growth happen due to creative destruction? Must the government subsidise the R&D (research & development) of private companies? This year's (2025) Nobel Economics Prize winners Philippe Aghion and Peter Howitt answered these questions in their 1992 Econometrica paper 'A Model Of Growth Through Creative Destruction' (17k+ citations). They derived the equations for the Equilibrium Rate of Creative Destruction (ERCD) for two scenarios:
A. Free market situation (pic: top equation)
B. Social optimal solution (pic: bottom equation)
z* = ERCD = Probability of a firm making a product of better quality (0<z*<1)
('SP' in bottom equation = Social Planner)
α = Marginal cost = Units of intermediate product used to make one unit of final product (0<α<1)
β = Discount factor = Weightage people give to future consumption (0<β<1)
γ = Innovation step size = Increase in product quality (γ>1)
ψ = R&D productivity (ψ>0)
L = Total amount of labour
The two equations are different - so the free market ERCD and the social optimal ERCD are NOT the same. There are 3 differences:
1. Top equation: Numerator's first term has γ. Bottom equation: Numerator's first term has (γ−1) - which is <γ. So bottom equation's z* < top equation's z*. So social optimal ERCD < free market ERCD. Why? Consider an old firm selling a product of a certain quality and making profit P1. Then a new firm innovates and makes a product of better quality. Now this new product will completely replace the old product in the market. Thus the old firm now makes zero profit and the new firm makes profit P2 (P2>P1). So the new firm's incentive to innovate is the entire amount P2. But the gain to society is just the difference in quality between the two products - given by P2-P1 (<P2). Thus firms innovate at a faster rate than is socially optimal. That is, free market ERCD > social optimal ERCD.
2. Top equation: Denominator has an extra +β. So top equation's z* < bottom equation's z*. So free market ERCD < social optimal ERCD. Why? Because the free market ERCD is decided only by the firms trying to maximise their own profits. But society gives weightage to the future, and hence to innovation - thus increasing the social optimal ERCD. And the more this weightage, the more important is innovation - and the higher is the social optimal ERCD.
3. Bottom equation: Numerator's first term has α^[-1/(1-α)]. Since α<1, this term is >1. So bottom equation's z* > top equation's z*. So social optimal ERCD > free market ERCD. This is because monopolistic firms charge too high prices and hence under-use the intermediate products.
Thus #1 makes free market ERCD > social optimal ERCD. And #2 and #3 make free market ERCD < social optimal ERCD. The relationship is decided by the values of the parameters α, β, γ, ψ and L. If free market ERCD < social optimal ERCD, then government must subsidise R&D - in order to increase the ERCD from the free market level to the social optimal level . . .
